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On mean-based bivariate Birnbaum-Saunders distributions: Properties, inference and application

Author

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  • Helton Saulo
  • Jeremias Leão
  • Roberto Vila
  • Victor Leiva
  • Vera Tomazella

Abstract

Birnbaum-Saunders models have been widely used to describe data following positive-skew distributions. In this article, we introduce a bivariate Birnbaum-Saunders distribution which has the mean as one of its parameters, allowing us to mimic the standard parameterization of the normal distribution, but in an asymmetric framework. We derive some properties of the mean-based bivariate Birnbaum-Saunders distribution useful for statistical and reliability analyses. Maximum likelihood and modified moment estimations of the model parameters and associated inference are considered. A simulation study is conducted to evaluate the performance of the corresponding estimators and coverage probabilities of confidence intervals are also discussed. Finally, a real-world data analysis is carried out for illustrating the potential of the proposed model.

Suggested Citation

  • Helton Saulo & Jeremias Leão & Roberto Vila & Victor Leiva & Vera Tomazella, 2020. "On mean-based bivariate Birnbaum-Saunders distributions: Properties, inference and application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(24), pages 6032-6056, December.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:24:p:6032-6056
    DOI: 10.1080/03610926.2019.1626425
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    Cited by:

    1. Luis Sánchez & Víctor Leiva & Manuel Galea & Helton Saulo, 2020. "Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    2. Jimmy Reyes & Jaime Arrué & Víctor Leiva & Carlos Martin-Barreiro, 2021. "A New Birnbaum–Saunders Distribution and Its Mathematical Features Applied to Bimodal Real-World Data from Environment and Medicine," Mathematics, MDPI, vol. 9(16), pages 1-19, August.

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